Effects of orbital angular momentum on few-cycle and sub-cycle pulse shapes: coupling between the temporal and angular momentum degrees of freedom

Abstract

We describe the coupling between orbital angular momentum (OAM) and temporal degrees of freedom in pulsed Laguerre-Gauss beams. The effects of this coupling are to increase significantly the duration of few-cycle pulses when the OAM carried by the pulse is large, and to enhance spatiotemporal couplings. Contrary to other detrimental but retrievable effects such as spatial, group velocity and topological charge dispersions in these pulses, OAM-temporal coupling effects are unavoidable, and have therefore an impact in applications such as OAM-based optical communications, or in the generation of vortex-carrying attosecond pulses.

Generation of Terawatt-Scale Vortex Pulses Based on Optical Parametric Chirped-Pulse Amplification

“…A comparison of these pulses reveals that the amplification does not affect the compressed pulse width. Moreover, for a pulse of 30 fs scale and low topological charge (l = 1), the effect of the spiral wavefront on the pulse time-domain width can be ignored [35], [36]. Typically, a shorter pulse could be obtained using a specially designed compressor system and active pulse sharper for dispersion management [37].…”

Attosecond helical pulses

“…Another important issue is the duration of the individual pulses in the helical structure. As recently found, [7,8] a pulsed vortex with well-defined topological charge, i. e., without topological charge dispersion, must be longer than a certain minimum value determined by the topological charge. Helical pulses are superpositions of pulsed vortices with carrier frequencies in a frequency comb and with topological charges varying linearly with frequency, and therefore present topological charge dispersion.…”

“…The real quadratic term r 2 /2cR(z) represents a time delay for the whole helical pulse structure to reach the distance z at a radius r due to the spherical pulse fronts of radius R(z) when the pulse is converging to or diverging from the waist, as for the fundamental pulsed Gaussian beam [10,13]. The dependence of the imaginary part on l 0 reflects the coupling between the OAM and temporal degrees of freedom, as recently described [8,17]. If the phases ofã j are approximately constant, a(t) represents a train of pulses with repetition period δt = 2π/δjδω, where δj is the step in the index j, e. g., δj = 2 in high harmonic generation experiments.…”

“…The above upper bound for the pulse bandwidth implies that an arbitrarily short pulse cannot carry a vortex of the topological charge l, but there is lower bound to its duration [7,8]. As shown below, the dispersion or uncertainty in the topological charge inherent to the helical pulses will allow to beat these upper and lower bounds of the spectral bandwidth and pulse duration.…”

Broadband X-waves with orbital angular momentum

“…Most of this research is focused on localized waves without orbital angular momentum (OAM) [2-5], and more recently on synthesizing one-dimensional localized waves, or space-time light sheets [6,7], which cannot carry OAM. This fact could seem surprising since the interest in OAM of light started and developed over the same decades, at first for monochromatic light [8,9], and later for ultrashort pulses [10][11][12][13][14]. Only recently vortex-carrying X-waves and other diffraction-free pulses with OAM have started to gain attention [15][16][17][18][19].…”